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The Banach algebra of conservative triangular matrices. (English) Zbl 0469.40001


MSC:

40C05 Matrix methods for summability
40G99 Special methods of summability
40H05 Functional analytic methods in summability
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References:

[1] Agnew, R.P.: Equivalence of Methods for Evaluation of Sequences. Proc. Amer. Math. Soc.3, 550-556 (1952) · Zbl 0047.06502 · doi:10.1090/S0002-9939-1952-0048600-5
[2] Berg, I.D.: A Banach Algebra Criterion for Tauberian Theorems. Proc. Amer. Math. Soc.15, 648-652 (1964) · Zbl 0131.05701 · doi:10.1090/S0002-9939-1964-0165285-6
[3] Berg, I.D.: Open Sets of Conservative Matrices. Proc. Amer. Math. Soc.16, 719-724 (1965) · Zbl 0139.08304 · doi:10.1090/S0002-9939-1965-0179514-7
[4] Copping, J.: Mercerian Theorems and Inverse Transformations. Studia Math.21, 177-194 (1962) · Zbl 0121.05604
[5] Hogan, D.A., Kelly, E.P., Jr.: Bounded, Conservative, Linear Operators, and the Maximal Group. Proc. Amer. Math. Soc.32, 195-200 (1972) · Zbl 0204.45501 · doi:10.1090/S0002-9939-1972-0290136-3
[6] Rhoades, B.E.: Triangular Summability Methods and the Boundary of the Maximal Group. Math. Z.105, 284-290 (1968) · Zbl 0179.08801 · doi:10.1007/BF01125969
[7] Sharma N.K.: Spectra of Conservative Matrices. Proc. Amer. Math. Soc.35, 515-518 (1972) · Zbl 0261.40002 · doi:10.1090/S0002-9939-1972-0306769-1
[8] Whitley, R.: Conull and Other Matrices which Sum a Bounded Divergent Sequence. Math. Monthly74, 798-801 (1967) · Zbl 0182.46401 · doi:10.2307/2315795
[9] Wilansky, A.: Topological Divisors of Zero and Tauberian Theorems. Trans. Amer. Math. Soc.113, 240-251 (1964) · Zbl 0182.46302 · doi:10.1090/S0002-9947-1964-0168967-X
[10] Wilansky, A., Zeller, K.: Banach Algebra and Summability. Illinois J. Math.2, 378-385 (1958) · Zbl 0082.27302
[11] Yood, B.: Transformations Between Banach Spaces in the Uniform Topology. Ann. of Math. (2)50, 486-503 (1949) · Zbl 0034.06401 · doi:10.2307/1969464
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